The "Hot Spots" Conjecture on Homogeneous Hierarchical Gaskets

The "Hot Spots" Conjecture on Homogeneous Hierarchical Gaskets

Year:    2018

Analysis in Theory and Applications, Vol. 34 (2018), Iss. 4 : pp. 374–386

Abstract

In this paper, using spectral decimation, we prove that the "hot spots" conjecture holds on a class of homogeneous hierarchical gaskets introduced by Hambly, i.e., every eigenfunction of the second-smallest eigenvalue of the Neumann Laplacian (introduced by Kigami) attains its maximum and minimum on the boundary. 

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-2017-0070

Analysis in Theory and Applications, Vol. 34 (2018), Iss. 4 : pp. 374–386

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Neumann Laplacian ”hot spots” conjecture homogeneous hierarchical gasket spectral decimation analysis on fractals.